Pith Number

pith:7Y3DCCWJ

pith:2018:7Y3DCCWJHM7VQ53YNQ3CFOZ4Z2

not attested not anchored not stored refs pending

Weighted cogrowth formula for free groups

Johannes Jaerisch, Katsuhiko Matsuzaki

arxiv:1802.08361 v1 · 2018-02-23 · math.DS · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Y3DCCWJHM7VQ53YNQ3CFOZ4Z2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:22:43.882973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe36310ac93b3f5877786c3622bb3cceaf90acdcccf5603554608327cf7bdf0b

Aliases

arxiv: 1802.08361 · arxiv_version: 1802.08361v1 · doi: 10.48550/arxiv.1802.08361 · pith_short_12: 7Y3DCCWJHM7V · pith_short_16: 7Y3DCCWJHM7VQ53Y · pith_short_8: 7Y3DCCWJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7Y3DCCWJHM7VQ53YNQ3CFOZ4Z2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fe36310ac93b3f5877786c3622bb3cceaf90acdcccf5603554608327cf7bdf0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3981d8fdf8abd8631e8f845d408378b4b403fe280f743535499209b095b3f35",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-02-23T02:04:39Z",
    "title_canon_sha256": "ee1327f34f536d1ad21aa859cb34f0a3942a5654bcaa26d5a680d48eca4b577b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.08361",
    "kind": "arxiv",
    "version": 1
  }
}